We only apply Q-learning ([1]} [1]}) as the reinforcement learning algorithm to enhance LKH rather than the variable strategy reinforcement method ([3]} [3]}), because the number of iterations of LKH in RHGA is small, so that the variable strategy method has little impact when it is applied to RHGA. Q-LKH applies Q-learning to learn to adjust the Q-value so as to estimate the state-action function more accurately. The Q-value is updated as follows:
\(Q(s_t,a_t)=(1-\lambda )\cdot {Q(s_t,a_t)}+\lambda \cdot [r(s_t,a_t)+\gamma {\max \limits _{a^{\prime }}Q(s_{t+1},a^{\prime })}],\) 
